Question
Explain relative velocity between two objects moving in a plane.
✓
Answer
- If $\vec{v}_A$ and $\vec{v}_B$ be the velocities of two bodies then relative velocity of A with respect to B is given by,$\vec{v}_{A B}=\vec{v}_A-\vec{v}_B$
- Similarly, the velocity of B with respect to A is given by, $\vec{v}_{ BA }=\vec{v}_{ B }-\vec{v}_A$
- Thus, the magnitudes of the two relative velocities are equal and their directions are opposite.
- For a number of objects A, B, C, D—Y, Z, moving with respect to the other. The velocity of A relative to Z can be given as, $\vec{v}_{ AZ }=\overrightarrow{ v }_{ AB }+\overrightarrow{ v }_{ BC }+\overrightarrow{ v }_{ CD }+\ldots+\overrightarrow{ v }_{ XY }+\overrightarrow{ v }_{ YZ }$
The order of subscripts is: A → B → C → D → Z
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